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There are two large parallel metallic pl...

There are two large parallel metallic plates `S_(1)` and `S_(2)` carrying surface charge densities `sigma_(1)` and `sigma_(2)` respectively `(sigma_(1) gt sigma_(2))` placed at a distance d apart in vacuum. Find the work done by the electric field in moving a point charge q at distance `a(a lt d)` from `S_(1)` towards `S_(2)` along a line making an angle `pi//4` with the normal to the plates.

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The correct Answer is:
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Electric field near a large metallic plate is given by `E = sigma // epsi_(0)`. In between the plates two fields will be in opposite directions. Hence
`E_("net") = (sigma_(1) - sigma_(2))/(epsi_(0)) = E_(0)` (say) , Now (potential difference )
` = q ( E_(0) a cos 45^(@) ) = (q) ((sigma_(1) - sigma_(2))/(epsi_(0))) (a)/(sqrt(2)) = ((sigma_(1) - simga_(2)) qa)/(sqrt(2) epsi_(0))`.
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